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I just wonder what these simple equations are called in English? Do they have professional names/terminologies in math?

equation 1: x = a + b - c

equation 2: x = a * b / c

The key is the sign, equation 1 only contains plus and/or minus signs. Equation 2 contains only Multiplication and division signs. a, b, and c are variables, they could be a complex term, or a single known or unknown value.

So, what do I call these two types of equations in English? I know the first one might be called a linear equation, but how about the second one?

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  • The second type used to be known as "quadratic equations" when I was at school - but that was a very long time ago! The first type looks like a simple equation - though if there really are four unknowns, you are way beyond me.
    – WS2
    Aug 5, 2022 at 6:48
  • Have you checked the bilingual dictionary?
    – James K
    Aug 5, 2022 at 7:48
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    @WS2 a quadratic equation is one where a term is squared (multiplied by itself). The term derives from the latin quadratus (made square). The second equation is not a quadratic equation, because no term is multiplied by itstelf. Both are linear equations cuemath.com/algebra/linear-equations
    – JavaLatte
    Aug 5, 2022 at 10:14
  • @JavaLatte Apologies - it's been a long time!
    – WS2
    Aug 5, 2022 at 13:12
  • @javalatte the second equation is also a linear equation?
    – Elizabeth
    Aug 5, 2022 at 15:06

3 Answers 3

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Looking at the expressions on the right-hand-side of the two formulae:

The first expression is a sum of three terms: a, b and -c.

Longer sums (especially when written with Σ notation) are also called series.

The second expression is product of three factors a, b and c-1

What about "linear equations". Well this is maths, not English learning. An equation is linear if it is in the form y = A x (where "A" is a constant (possibly a matrix), and x and y are (possibly vector) variables), or in some contexts if y=ax + b. However you say that a, b, c "could be a complex term, or a single known or unknown value." and so these equations are not in general linear.

If you consider x,a,b and c all to be variables, then "x = a+b+c" is linear (it could be written in matrix form x = (1 1 1)(a b c)T) The second is not linear, or non-linear.

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  • thank you so much! Clearly, the question is more complicated than I thought. Yes, I'll go for 'linear' and 'non-linear' with some extra explanation about the formulas.
    – Elizabeth
    Aug 5, 2022 at 17:11
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The expression on the right-hand side of the first equation (a + b - c) is a "trinomial", and the expression on the right-hand side of the second (a * b / c) is a "monomial". (You could therefore call the equations a "trinomial equation" and a "monomial equation", but those expressions aren't very common.)

The equations can also be classified according to their degree, and I think that some people have gotten confused because you don't specify what a, b, and c are.

  • If all three letters are constants, then both equations are constant.
  • If either a or b is a variable (and the other two letters are constants), then both equations are linear.
  • If at least two of those letters are variables, then the first equation is linear but the second isn't.
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These are arithmetic expressions and you could say arithmetic equations or arithmetical equations if you needed to insist that they are equations.

The first example is in Presburger_arithmetic and the second in Peano arithmetic, which are theories of the natural numbers, but both are highly technical and wouldn't be understood by a general audience

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    This answer assumes that these are assignment in a computer language, but the OP mentions maths, the reference to Presburger and Peano arithmetic is confusing and incorrect. There is no suggestion or requirement that a, b, c represent natural numbers. Peano arithmetic has no "division" operation. There is no technical nor colloquial context in which you would say "a * b / c is an expression in Peano arithmetic"
    – James K
    Aug 5, 2022 at 9:59
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    In mathematics, there is a distinct difference between equation and expression and the two terms cannot be used interchangeably. An equation has an equals sign, an expression does not.
    – Canadian Yankee
    Aug 5, 2022 at 12:38

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